Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. (of a subset) the least element of the containing set that is greater or equal to all elements of the subset. The supremum may or may not be a member of the subset.

Etymologies

Sorry, no etymologies found.

Examples

  • We call the supremum the join and the infimum the meet of the elements a

    Citizendium, the Citizens' Compendium - Recent changes [en]

  • A '' supremum '' for '' S '' is an upper bound which is less than or equal to any other upper bound for '' S ''; an '' infimum '' is a lower bound for '' S '' which is greater than or equal to any other lower bound for '' S ''.

    Citizendium, the Citizens' Compendium - Recent changes [en]

  • The least upper bound is also sometimes called the "supremum", abbreviated "sup".

    Conservapedia - Recent changes [en]

  • The use of the word “super” is derived from the same root as “supremum”, which for a given set refers to the “least upper bound” of the set, or basically the smallest element that has value greater (in some measurable sense) than every element within the set.

    Matthew Yglesias » Supergroups

  • (D, ‰¤) into a complete lattice (E, ‰¤) is said to be continuous when it preserves the supremum of each ideal on

    Combinatory Logic

  • ˆˆ C, that is, provided that the supremum of I is an element of C. (For example, complements of principal ideals are open.) f turns out to be continuous in the usual topological sense, that is, the inverse image of an open set being open, when D and E are taken together with their topologies.

    Combinatory Logic

  • [4629] Miseriquid luctatiunculis hisce volumus? ecce mors supra caput est, et supremum illud tribunal, ubi et dicta et facta nostra examinanda sunt: Sapiamus!

    Anatomy of Melancholy

  • The last two lines of the second verse stated that the Father had entrusted to Christ, as His right, "absolute dominion over the peoples" Cui iure sceptrum gentium Pater supremum credidit.

    The Reign of Christ the King

  • L2 presented in different ways, it is always possible to extract the respective consequence relations and then combine them (taking, for instance their supremum in an appropriate lattice of consequence relations).

    Combining Logics

  • That is we consider a confidence region of fits based on the statistics and we plot the supremum (least upper bound) and infimum (greatest lower bound) of all these fits.

    More on MBH98 Figure 7 « Climate Audit

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